Anisotropic Energy-Gaps of Iron-based Superconductivity from Intra-band Quasiparticle Interference in LiFeAs

Cooper pairing in the iron-based high-$T_C$ superconductors is thought to occur due to the projection of the antiferromagnetic interactions between neighboring iron atoms onto the complex momentum-space electronic structure. A key consequence is that distinct anisotropic energy gaps $\Delta_i(k)$ with specific relative orientations should occur on the different electronic bands $i$. However, the high-precision spectroscopy required to demonstrate anisotropy of the energy gaps, and to determine the relationship between the $\Delta_i(k)$ on different bands, has not been achieved. Here we introduce intra-band Bogoliubov quasiparticle scattering interference (QPI) to iron-based superconductor studies, focusing specifically on LiFeAs. This approach provides direct spectroscopic confirmation of multiple anisotropic energy gaps on different bands. We identify the QPI signatures of the three hole-like bands assigned by photoemission studies to be $\gamma$, $\alpha_2$ and $\alpha_1$. Then, by introducing a new QPI technique, we determine the magnitude and relative orientations of the anisotropic $\Delta_i(k)$. Intra-band Bogoliubov QPI therefore yields the spectroscopic information required to identify the mechanism of superconductivity in iron-based superconductors.